Choose the correct answer. NOTE: Figures are not drawn to ...

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ACT Geometry Review Problems

Choose the correct answer. NOTE: Figures are not drawn to scale.

1. In the figure, AC = 24, AB = 6x ? 6, BC = 5x ? 3 and BE = 3x + 2. Which do you know is true?

I. AC bisects DE. II. DE bisects AC. III. DE bisects AC.

? D

? B?

A

C

? E

a) I only b) II only

c) III only

d) I and II only

e) II and III only

2. Find the values of x and y.

a) x = 20, y = 34

b) x = 10, y = 52

c) x = 12, y = 18

d) x = 11, y = 7

(11x + 3)? (4x ? 3)? (2y + 9)?

3. In the figure, BD bisects ABE, BE bisects ABG, mEBF = 37, and mCBG = 44.

Find mDBF.

a) 68

b) 34

c) 82

d) 71

? E D ?

F ? ? G

?

?

?

A

B

C

4. ABC and CBD are adjacent congruent angles, and mABD = 160. What are the two possible measures for ABC?

a) 80, 160

b) 100, 160

c) 80, 100

d) 90, 180

e) 160, 200

5. Find mADC.

a) 53

b) 43

c) 137

d) 127

A (x + 10)?

!

B

! (3x - 2)?

D

C

6. If AB || CD, AB = CD and AF = FD = DE. What can you conclude? B I. ABF DCE

II. ABF DBF

III. DBF DCE

A

F

a) I only b) II only c) III only d) I, II and III

C

D

E

7. The ratio of the measures of two supplementary angles 7:8. Which proportion(s) could you use to find the measures of the angles?

x 7 I. =

y8

x 8 II. =

y7

x 7

III.

=

180 - x 8

x 8

IV.

=

180 - x 7

a) I only b) II only

c) I and II only

d) III and IV only e) I, II III, and IV

8. Quad. ABCD ~ Quad. HGFE. Find the perimeter of ABCD.

a) 88

b) 22

c) 66

d) 31

A 21

12

B

D E

3

C F

H

4

G 8

9. A ladder 6 m long just reaches the top of a building and its foot makes a 76? angle with the

ground. Which of the following equations could be used to calculate the height, h, of the

building?

h

I. sin 76? =

II. 6 cos14? = h

6

h III. cos 76? =

6

a) I only b) II only c) III only

10. Find the measure of AB.

a) 34

b) 26

c) 86

d) I and II only e) I, II and III

d) 76

100? A

87?

67? B

140?

11. A square garden enclosed by a fence with perimeter 40 m is to be expanded so it includes 300 m2 more area but is still square. If the gardener can reuse the old fence pieces, what length of new fence must the gardener buy?

a) 10 m b) 20 m c) 40 m d) 100 m

12. A rectangular garden has dimensions 30 feet by 20 feet. What is the area of the 2 foot wide walkway around the garden?

a) 104 ft2 b) 216 ft2

c) 680 ft2

d) 704 ft2 e) 1416 ft2

13. In two hours, the minute hand of a clock rotates through an angle equal to which of the following?

a) 90

b) 180

c) 360

d) 720

e) 1080

14. AB is the diameter of a circle whose center is at P. What are the coordinates of B?

a) (10, 7) b) (5, 2.5) c) (12, 7) d) (11, 8) e) (11, 7)

A (3, 2)

B

? P (7,5)

15. In ABC, mA = 23 and mB = 84. What is the longest side of ABC?

a) AC

b) AB

c) BC

d) AC AB (there is no longest side)

16. Given that mOAB = 45?. What is the area of the shaded portion of the circle?

A

a) 32 -16 2

b) 4 - 8 c) 32 - 8

d) 8 - 16

e) 8 - 8

O 42

B

17. What is the degree measure of ABC?

a) 45? d) 135?

b) 100? e) 160?

c) 110?

?

A 25? C

?

135?

?

B

C

18. A 65-foot ladder is leaning against a wall. Its lower end is 25 feet away from the wall. How much farther away will it be if the upper end is moved down 8 feet?

a) 39 ft b) 52 ft c) 14 ft d) 10 ft e) 8 ft

19. If point R has coordinates (x, y) and point S has coordinates (x + 1, y + 1), what is the distance between R and S?

a) 2

b) x 2 + y 2

c) 2 d) x 2 + y 2 + 2

e) x + y + 1

20. Will is standing 40 yards due North of point P. Grace is standing 60 yards due West of point P. What is the shortest distance between Will and Grace?

a) 20 yds b) 20 13 yds c) 80 13 yds d) 4 13 yds e) 80 yds

21. The circle in the figure is inscribed in a square with a perimeter of 20 inches. What is the area of the shaded regions?

22. A trapezoidal flower garden is shown below. What is the area of the garden?

23. In the figure below, x = ? a) 45 b) 60 c) 90 d) 105 e) 120

10 m 9 m

13 m

x ! y

30?

24. In the figure below, l1 is parallel to l2. Which of the following must be true?

I. w = a II. y + b = 180? III. x + d = 180?

l3

w? x?

l1

z? y?

a) I only

b) II only c) I and II only

d) II and III only e) I, II and III

a? b? d? c?

l2

Use the picture of ABC to answer questions 25 ? 28.

25. In the figure, AB = ?

a) 2

b) 2 3 c) 4

d) 4 2 e) 8

26. What is the ratio for sinB.

3

4

a)

b)

c) 45?

5

5

34 d)

5

e) 3 34

27. What is the ratio for tanC?

3

5

4

a)

b)

c)

4

3

3

34 d)

3

3 e)

34

28. Find the measure of B.

a) 90

b) 36.9 c) 53.1

d) 30.9

e) 45

B 5

A

C

3

29. In the figure, what is the sum of the indicated angles? a) 540 b) 720 c) 900 d) 1,080 e) 1,260

30. If the area of a circle is 9, which of the following is(are) true? I. The radius is 3. II. The diameter is 6. III. The circumference is 6.

a) I only b) II only c) III only d) I and II only e) I, II and III

31. In the figure, if QRST is a square and PQ =

a) 2

b) 6

c) 2 2

d) 4

e) 4 3

2 , what is the length of RU?

Q

R

45?

P !

45?

T

S

32. Use the figure to find the length of BC.

a) 1

b) 2

c) 3

d) 4

e) 5

33. What is 2x ? 60 equal to?

a) 80

b) 40

c) 30

d) 20

e) 10

B

13 ! C

A ! 4 2

23

D

2x

x

60?

30? U

34. A triangle has sides with lengths 12, 14 and 20 is similar to a 2nd triangle that has 1 side with length of 40. What is the smallest possible perimeter of the 2nd triangle?

a) 48

b) 92

c) 120

d) 160

e) 180

35. In the figure below, all distances are in centimeters and all angles are right angles. What is the

length, in centimeters, of segment AC?

A 5

a) 30 2

b) 50

c) 75

10

d) 60 2

e) 100

10

5 20

30 5 5

10

B

C

40

ACT Geometry Review Answers:

1) B 2) C

not enough info to tell BD!BD be sure, never assume! linear pair

3) D straight line = 180

4) C 160 /2 and 360-160 then /2

5) D Same Side Interior angles (only if parallel lines! Look for arrows)

6) A Mark sides with tick marks. Look for corresponding angles.

7) D 7x + 8x = 180

8) C ratio is 12:4

9) D SOHCAHTOA

10)C inscribed angles

11) C add old and new area and find the sides.

12)B outside area minus inside area 13)D minute hand goes around the full circle twice

14)D midpoint formula

15)A longest side is across from the largest angle

16)D ? area of the circle minus the area of the triangle

17) C

remote interior angle theorem or linear pair & add 2 s then subtract from 180

18)C Pythagorean theorem (make sure you subtract!)

19) A distance formula

20) B Pythagorean theorem

21) 25-6.25 (or 5.37) 22) 123.5 m2

23) E Right angle = 90 and linear pair 24) C Alternate Interior, Corresponding, Alternate Exterior, Same Side Interior

25) C Pythagorean theorem

26) A SOHCAHTOA

27) C SOHCAHTOA 28) B SOHCAHTOA (press 2nd on your calculator. Calculator in degree mode.)

29) C (n-2)180 (sum of the interior angles) 30) E Area of circle = r2, Circumference = 2r

31) D 45-45-90 and 30-60-90 triangles

32) B Pythagorean theorem

33) D straight line = 180 and vertical angles are !. Plug x in to 2x-60

34) B 40 20 so each side is twice as big 35) B Pythagorean theorem

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